How to Add and Subtract
Positive and Negative Numbers
Numbers Can be Positive or Negative:
Negative Numbers (−)  Positive Numbers (+) 
(This is the Number Line, read about Using The Number Line) 
"−" is the negative sign.  "+" is the positive sign 
No Sign Means Positive
If a number has no sign it usually means that it is a positive number.
Example: 5 is really +5
Adding Positive Numbers
Adding positive numbers is just simple addition.
Example: 2 + 3 = 5
is really saying
"Positive 2 plus Positive 3 equals Positive 5"
You could write it as (+2) + (+3) = (+5)
Subtracting Positive Numbers
Subtracting positive numbers is just simple subtraction.
Example: 6 − 3 = 3
is really saying
"Positive 6 minus Positive 3 equals Positive 3"
You could write it as (+6) − (+3) = (+3)
Balloons and Weights
This basket has balloons and weights tied to it:

Here is what adding and subtracting positive numbers looks like:
You can add balloons (you are adding positive value) the basket gets pulled upwards (positive) 
You can take away balloons (you are subtracting positive value) the basket gets pulled downwards (negative) 
Now let's see what adding and subtracting negative numbers looks like:
You can add weights (you are adding negative values) the basket gets pulled downwards (negative) 
And you can take away weights (you are subtracting negative values) the basket gets pulled upwards (positive)

That last one was interesting ... subtracting a negative made the basket go up
Subtracting a Negative is the same as Adding 
Example: What is 6 − (−3) ?
6−(−3) = 6 + 3 = 9
Example: What is 14 − (−4) ?
14−(−4) = 14 + 4 = 18
We also found that taking away balloons (subtracting positives) or adding weights (adding negatives) both made the basket go down.
And Positive and Negative Together ...
Subtracting a Positive or Adding a Negative is Subtraction 
Example: What is 6 − (+3) ?
6−(+3) = 6 − 3 = 3
Example: What is 5 + (−7) ?
5+(−7) = 5 − 7 = −2
The Rules:
It can all be put into two rules:
Rule  Example  

Two like signs become a positive sign  +(+)  3+(+2) = 3 + 2 = 5  
−(−)  6−(−3) = 6 + 3 = 9  
Two unlike signs become a negative sign  +(−)  7+(−2) = 7 − 2 = 5  
−(+)  8−(+2) = 8 − 2 = 6  
They are "like signs" when they are like each other (in other words: the same).
So, all you have to remember is:
Two like signs become a positive sign
Two unlike signs become a negative sign
Example: What is 5+(−2) ?
+(−) are unlike signs (they are not the same), so they become a negative sign.
5+(−2) = 5 − 2 = 3
Example: What is 25−(−4) ?
−(−) are like signs, so they become a positive sign.
25−(−4) = 25+4 = 29
Example: What is −6+(+3) ?
+(+) are like signs, so they become a positive sign.
−6+(+3) = −6 + 3 = 3
Start at −6 on the number line, move forward 3, and you end up at −3
Now Play With It!
Try playing Casey Runner, you need to know the rules of positive and negative to succeed! 
A Common Sense Explanation
And there is a "common sense" explanation:
If I say "Eat!" I am encouraging you to eat (positive)
But if I say "Do not eat!" I am saying the opposite (negative).
Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).
So, two negatives make a positive, and if that satisfies you, then you are done!
Another Common Sense Explanation
A friend is +, an enemy is −
+ + ⇒ +  a friend of a friend is my friend  
+ − ⇒ −  a friend of an enemy is my enemy  
− + ⇒ −  an enemy of a friend is my enemy  
− − ⇒ +  an enemy of an enemy is my friend 
A Bank Example
Example: You have $80 in your account right now.
Last year the bank subtracted $10 by mistake, and they want to fix it.
So the bank must take away a negative $10:
$80−(−$10) = $80 + $10 = $90
So you get $10 more in your account.
Another Example You Might Like
Ally's Points
Ally can be naughty or nice. So Ally's parents have said "If you are nice we will add 3 points (+3). Ally starts the day with 9 Points: 

So if you subtract a negative, you gain points
(i.e. the same as adding points).
So Subtracting a Negative is the same as Adding 

See: both "15 − (+3)" and "15 + (−3)" result in 12.
So:
It doesn't matter if you subtract positive points
or add negative points,
you still end up losing points.
So, Subtracting a Positive or Adding a Negative is Subtraction 
Try These Exercises ...
Now try This Worksheet, and see how you go.
And also try these questions: